Question

State true or false.
The sum of a number and its opposite is zero.
A. True
B. False

Answer 1

Hint: We’ll discuss the arithmetic and its property related to addition, subtraction, and multiplication and how they are used for the simplification here or the general method to solve the arithmetic problems, here we’ll just learn about the addition of two numbers. Using the arithmetic method for the addition of two numbers we’ll solve our problem to get the required answer.

Complete step by step answer:

Arithmetic is a branch of mathematics that deals with the numbers and its operations like addition, subtraction, multiplication, division, exponentiation, and extraction of roots.
Summation or subtraction of two numbers is also dependent on the sign of the two numbers, if the sign of both the numbers is the same then the summation has to take place with the sign that the two numbers have, and if the two numbers have different signs then the subtraction has to be done with the sign of the greater number taken without the sign. So here we have given that two numbers are added having equal magnitude but the different sign, the subtraction should take place hence the will be zero and the statement is true.
Option(A) is correct.

Note: We can also solve this with the help of number line as

Here we can see that every number and its opposite are equidistant from the origin hence the magnitude is the same but the opposite sign giving the sum will be zero.
Here we have taken example of 4a and -4a as $4a + ( - 4a) = 0$.